What is the equation of the line with slope # m= 13/7 # that passes through # (7/5,4/7) #?

1 Answer
Alan P.
Dec 17, 2015

#65x-35y=71#

Explanation:

Given a slope #m# and a point #(barx,bary)#
the "slope-point form" of the linear equation is
#color(white)("XXX")(y-bary)=m(x-barx)#

Given
#color(white)("XXX")m=13/7#
and
#color(white)("XXX")(barx,bary)=(7/5,4/7)#

The "slope-point form" would be:
#color(white)("XXX")(y-4/7)=13/7(x-7/5)#
and this should be a valid answer to the given question.

However, this is ugly, so let's convert it into standard form:
#color(white)("XXX")Ax+By=C# with #A, B, C in ZZ, A>=0#

Multiply both sides by #7#
#color(white)("XXX")7y-4=13x-91/5#

Multiply both sides by #5# to clear the remaining fraction
#color(white)("XXX")35y-20=65x-91#

Subtract #(35y-91)# from both sides to get the variables on one side and the constant on the other
#color(white)("XXX")71=65x-35y#

Exchange sides:
#color(white)("XXX")65x-35y=71

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